Math.NumberTheory.Canon.Simple

This a wrapper for the Canonical Representation type found in the Internals module. If you want to work with arbitrarily nested prime towers, you can use the Math.NumberTheory.Canon module.

Documentation

newtype SimpleCanon

SimpleCanon is a new type wrapping a canonical representation.

Constructors

MakeSC CR_

Instances

Enum SimpleCanon

Methods

succ :: SimpleCanon -> SimpleCanon

pred :: SimpleCanon -> SimpleCanon

toEnum :: Int -> SimpleCanon

fromEnum :: SimpleCanon -> Int

enumFrom :: SimpleCanon -> [SimpleCanon]

enumFromThen :: SimpleCanon -> SimpleCanon -> [SimpleCanon]

enumFromTo :: SimpleCanon -> SimpleCanon -> [SimpleCanon]

enumFromThenTo :: SimpleCanon -> SimpleCanon -> SimpleCanon -> [SimpleCanon]

Eq SimpleCanon

Methods

(==) :: SimpleCanon -> SimpleCanon -> Bool

(/=) :: SimpleCanon -> SimpleCanon -> Bool

Fractional SimpleCanon

Methods

(/) :: SimpleCanon -> SimpleCanon -> SimpleCanon

recip :: SimpleCanon -> SimpleCanon

fromRational :: Rational -> SimpleCanon

Integral SimpleCanon

Methods

quot :: SimpleCanon -> SimpleCanon -> SimpleCanon

rem :: SimpleCanon -> SimpleCanon -> SimpleCanon

div :: SimpleCanon -> SimpleCanon -> SimpleCanon

mod :: SimpleCanon -> SimpleCanon -> SimpleCanon

quotRem :: SimpleCanon -> SimpleCanon -> (SimpleCanon, SimpleCanon)

divMod :: SimpleCanon -> SimpleCanon -> (SimpleCanon, SimpleCanon)

toInteger :: SimpleCanon -> Integer

Num SimpleCanon

Methods

(+) :: SimpleCanon -> SimpleCanon -> SimpleCanon

(-) :: SimpleCanon -> SimpleCanon -> SimpleCanon

(*) :: SimpleCanon -> SimpleCanon -> SimpleCanon

negate :: SimpleCanon -> SimpleCanon

abs :: SimpleCanon -> SimpleCanon

signum :: SimpleCanon -> SimpleCanon

fromInteger :: Integer -> SimpleCanon

Ord SimpleCanon

Methods

compare :: SimpleCanon -> SimpleCanon -> Ordering

(<) :: SimpleCanon -> SimpleCanon -> Bool

(<=) :: SimpleCanon -> SimpleCanon -> Bool

(>) :: SimpleCanon -> SimpleCanon -> Bool

(>=) :: SimpleCanon -> SimpleCanon -> Bool

max :: SimpleCanon -> SimpleCanon -> SimpleCanon

min :: SimpleCanon -> SimpleCanon -> SimpleCanon

Real SimpleCanon

Methods

toRational :: SimpleCanon -> Rational

Show SimpleCanon

Define various instances

Methods

showsPrec :: Int -> SimpleCanon -> ShowS

show :: SimpleCanon -> String

showList :: [SimpleCanon] -> ShowS

CanonConv SimpleCanon

Methods

toSC :: SimpleCanon -> SimpleCanon

toRC :: SimpleCanon -> RationalSimpleCanon

type SC = SimpleCanon

Shorthand type declaration

toSimpleCanon :: CanonConv a => a -> SimpleCanon

Convert CanonConv types to SimpleCanon.

toSC :: CanonConv c => c -> SimpleCanon

Convert a type to a SimpleCanon.

toSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> SimpleCanon

This function allow you to specify a user function when converting a canon rep to an SC.

fromSimpleCanon :: SimpleCanon -> CR_

Grab the canon rep from a SimpleCanon.

fromSC :: SimpleCanon -> CR_

Grab the canon rep from a SimpleCanon.

class CanonConv c where

Typeclass for converting to SimpleCanon and RationalSimpleCanon

Minimal complete definition

toSC, toRC

Methods

toSC :: c -> SimpleCanon

Convert a type to a SimpleCanon.

toRC :: c -> RationalSimpleCanon

Convert a type to a RationalSimpleCanon.

Instances

CanonConv CR_

Methods

toSC :: CR_ -> SimpleCanon

toRC :: CR_ -> RationalSimpleCanon

CanonConv RationalSimpleCanon

Methods

toSC :: RationalSimpleCanon -> SimpleCanon

toRC :: RationalSimpleCanon -> RationalSimpleCanon

CanonConv SimpleCanon

Methods

toSC :: SimpleCanon -> SimpleCanon

toRC :: SimpleCanon -> RationalSimpleCanon

scGCD :: SimpleCanon -> SimpleCanon -> SimpleCanon

SimpleCanon GCD and LCM functions

scLCM :: SimpleCanon -> SimpleCanon -> SimpleCanon

SimpleCanon GCD and LCM functions

scLog :: SimpleCanon -> Rational

Wrapper for underlying CR function

scLogDouble :: SimpleCanon -> Double

Wrapper for underlying CR function

scNegative :: SimpleCanon -> Bool

Wrappers for underlying canon rep functions

scPositive :: SimpleCanon -> Bool

Wrappers for underlying canon rep functions

scToInteger :: SimpleCanon -> Integer

Convert a SimpleCanon back to an Integer.

scToI :: SimpleCanon -> Integer

Convert a SimpleCanon back to an Integer.

newtype RationalSimpleCanon

Newtype for RationalSimpleCanon. The underlying canon rep is the same.

Constructors

MakeRC CR_

Instances

Enum RationalSimpleCanon

Methods

succ :: RationalSimpleCanon -> RationalSimpleCanon

pred :: RationalSimpleCanon -> RationalSimpleCanon

toEnum :: Int -> RationalSimpleCanon

fromEnum :: RationalSimpleCanon -> Int

enumFrom :: RationalSimpleCanon -> [RationalSimpleCanon]

enumFromThen :: RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon]

enumFromTo :: RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon]

enumFromThenTo :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon]

Eq RationalSimpleCanon

Methods

(==) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

(/=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

Fractional RationalSimpleCanon

Methods

(/) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

recip :: RationalSimpleCanon -> RationalSimpleCanon

fromRational :: Rational -> RationalSimpleCanon

Integral RationalSimpleCanon

Caveat: These functions will error out (in)directly if there are any negative exponents.

Methods

quot :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

rem :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

div :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

mod :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

quotRem :: RationalSimpleCanon -> RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon)

divMod :: RationalSimpleCanon -> RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon)

toInteger :: RationalSimpleCanon -> Integer

Num RationalSimpleCanon

Methods

(+) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

(-) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

(*) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

negate :: RationalSimpleCanon -> RationalSimpleCanon

abs :: RationalSimpleCanon -> RationalSimpleCanon

signum :: RationalSimpleCanon -> RationalSimpleCanon

fromInteger :: Integer -> RationalSimpleCanon

Ord RationalSimpleCanon

Methods

compare :: RationalSimpleCanon -> RationalSimpleCanon -> Ordering

(<) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

(<=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

(>) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

(>=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool

max :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

min :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon

Real RationalSimpleCanon

Methods

toRational :: RationalSimpleCanon -> Rational

Show RationalSimpleCanon

Define various instances for RationSimpleCanon.

Methods

showsPrec :: Int -> RationalSimpleCanon -> ShowS

show :: RationalSimpleCanon -> String

showList :: [RationalSimpleCanon] -> ShowS

CanonConv RationalSimpleCanon

Methods

toSC :: RationalSimpleCanon -> SimpleCanon

toRC :: RationalSimpleCanon -> RationalSimpleCanon

type RC = RationalSimpleCanon

Shorthand type name

toRationalSimpleCanon :: CanonConv a => a -> RationalSimpleCanon

Convert CanonConv types to RationalSimpleCanon.

toRC :: CanonConv c => c -> RationalSimpleCanon

Convert a type to a RationalSimpleCanon.

toRationalSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> RationalSimpleCanon

Convert canon rep to RationalSimpleCanon via a user-supplied criterion function.

fromRationalSimpleCanon :: RationalSimpleCanon -> CR_

Convert RC back to underlying canon rep.

fromRC :: RationalSimpleCanon -> CR_

Convert RC back to underlying canon rep.

rcNegative :: RationalSimpleCanon -> Bool

Wraps underlying canon rep functions.

rcPositive :: RationalSimpleCanon -> Bool

Wraps underlying canon rep functions.

getNumer :: RationalSimpleCanon -> SimpleCanon

Pulls numerator or denominator from RC and converts it to a SimpleCanon.

getDenom :: RationalSimpleCanon -> SimpleCanon

Pulls numerator or denominator from RC and converts it to a SimpleCanon.

getNumerDenom :: RationalSimpleCanon -> (SimpleCanon, SimpleCanon)

Wraps crSplit function and returns a pair of SimpleCanons.

getNumerAsRC :: RationalSimpleCanon -> RationalSimpleCanon

Calls underlying canon rep function.

getDenomAsRC :: RationalSimpleCanon -> RationalSimpleCanon

Calls underlying canon rep function.

getNumerDenomAsRCs :: RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon)

Wraps crSplit function and returns a pair of RationalSimpleCanons.

rcLog :: RationalSimpleCanon -> Rational

Calls underlying canon rep function.

rcLogDouble :: RationalSimpleCanon -> Double

Calls underlying canon rep function.

(>^) :: SimpleCanonRoot a b c => a -> b -> c infixr 9

Root Operator

(<^) :: SimpleCanonExpnt a b c => a -> b -> c infixr 9

Exponentiation Operator

(%) :: Integral a => a -> a -> a infixl 7

Modulus operator